"Our forces and the Iraqi forces have certainly disrupted Al Qaeda, probably to a level that we haven't seen at any time in my experience," said Dempsey, who served in Iraq in the initial stages as a division commander and later as head of the military organization in charge of training Iraqi security forces.
"They can regenerate, and do from time to time," he added in the interview in his office at Central Command headquarters.
Dempsey was in Iraq last week on a journey that also took him to Lebanon, where he consulted with the government and military commanders on their approach to dealing with Iranian-backed Hezbollah fighters.
In separate remarks at a military conference just a few miles from Dempsey's headquarters in Tampa, Defense Secretary Robert Gates said the Islamic extremist movements like Al Qaeda have been "built on an illusion of success" yet in some ways pose a more daunting challenge today than on Sept. 11, 2001.
Gates described these extremist groups as more diffuse and less reliant on a single figure like Usama bin Laden.
"It has become an independent force of its own, capable of animating a corps of devoted followers without direct contact," Gates told an international conference sponsored by U.S. Special Operations Command. He said this adversary is now "capable of inspiring violence without direct orders."
Dempsey, who was the Central Command deputy until Adm. William Fallon abruptly resigned amid reports that his views on Iran differed with those of the White House, is expected to remain as the acting commander until Gen. David Petraeus shifts from his post as top commander in Iraq, probably in September. Petraeus's Senate confirmation hearing is scheduled for Thursday.
Earlier Wednesday, the Army general who oversees U.S. commando operations in the Middle East said that Al Qaeda in Iraq has yet to be vanquished but is increasingly running out of places where local Iraqis will accommodate the group's extremist ideology.
"Is he still a lethal and dangerous threat to us? Absolutely," Maj. Gen. John Mulholland said in an interview with reporters at the headquarters of U.S. Special Operations Command, the organization with global responsibility for providing Army Green Berets, Navy SEALs and other commandos to combat terrorism.
Of the approximately 155,000 U.S. troops in Iraq, about 5,000 are special operations forces, who not only hunt and attack terrorist targets but also help train Iraqi security forces and work with local Iraqi governments.
Mulholland acknowledged that Al Qaeda, which U.S. intelligence says is led by foreign terrorists but is populated mainly by local Iraqis seeking to establish a radical Islamic state, still poses a major challenge in the Mosul area of northern Iraq and has occasionally slipped back into areas like Anbar province in western Iraq.
"Do we think he can at least try to regain a foothold in Anbar province? Yes, we do think he's trying to do that," Mulholland said.
While U.S. officials do not believe Al Qaeda is succeeding in re-establishing a significant presence in Anbar — which the group was forced to abandon a year ago as local Sunni Arabs turned violently against it — it does appear that small Al Qaeda cells can still slip into isolated areas and make trouble, he said.
"I don't want to paint a picture — or to convey to you in any way — that Al Qaeda in Iraq is being completely destroyed or rendered irrelevant, because that's not the case," he said. "They are still potentially a threat capable of death and destruction against the Iraqi people and our own forces there. But it is not something he can do easily any more."
Separately, Adm. Eric Olson, the commander of U.S. Special Operations Command, told a group of reporters that "the nature of the threat" posed by Iran's support for anti-U.S. forces in Iraq is unclear.
He made the remark in response to a question about the ability of U.S. special operations forces to meet the Iranian challenge.
"It's clear that there is some lethal aid originating from across the Iranian border," Olson said. "We can't say what the origin or the source of that is. So we are uncertain about our overall ability because we are uncertain of the nature of the threat. But I would say in general that special operations forces are well prepared and well equipped to meet the nation's expectations in that regard."